The change that we introduced by going from (REF ) and () to (REF ) and () is certainly drastic; the change is a departure from the microscopic description that we found based on the view of quasiparticles as neutral composites. In the case of bosons at filling factor one, Dong and Senthil showed that, on the basis of the Hartree-Fock description that is modified to include the \(SU(N)\)  invariance, in the manner of noncommutative field theory, an approximate commutative field theory description can be reached (via Seiberg-Witten map) in the form of Halperin-Lee-Read (HLR) [1]} description with a Chern-Simons (CS) term. This description cannot be viewed as a HLR theory (although of the same form), but as one that is based on the neutral composites (CFs) and limited to a LL, a description that is analogous to the description by composite bosons of the Laughlin case in [2]}.
In the case of electrons, in the half-filled LL, for which the Son's theory is relevant, one expects that, due to the requirement for the PH symmetry, a microscopic description will not generate a Chern-Simons term in an effective description. We encountered difficulties in the application of the program proposed by Dong and Senthil - to maintain the gauge invariance we consider constraints in the long-wavelength limit, which certainly implies changes in the microscopic physics, i.e., ultra-violet domain. We will find that the ensuing field theory will have a Chern-Simons term, but one may argue that now Pauli-Villars type of regularization is associated with the field theory, i.e., we have to treat the high-energy physics in a different way as opposed to the version of the Son's theory that was firstly proposed by Son, and assumes the dimensional regularization. Therefore, although we have done a drastic change in the microscopic domain, the theory may still make sense as a theory based on another kind of quasiparticle [3]}, [4]} and give a version of the Son's theory described in [5]}, [6]}, [7]}.
